
where the collision term on the right-hand side of the equation incorporates the effects of scattering due to impurities.
In the presence of electric (\(\mathbf {E}\) ) and magnetic (\(\mathbf {B}\) ) fields, the semiclassical dynamics of the Bloch electrons is [1]}
\(\dot{\mathbf {r}}^\chi &= \mathcal {D}^\chi \left( \frac{e}{\hbar }(\mathbf {E}\times \Omega ^\chi + \frac{e}{\hbar }(\mathbf {v}^\chi \cdot \Omega ^\chi ) \mathbf {B} + \mathbf {v}_\mathbf {k}^\chi )\right) \nonumber \\\dot{\mathbf {p}}^\chi &= -e \mathcal {D}^\chi \left( \mathbf {E} + \mathbf {v}_\mathbf {k}^\chi \times \mathbf {B} + \frac{e}{\hbar } (\mathbf {E}\cdot \mathbf {B}) \Omega ^\chi \right),\) 
